Timeline for Are there two non-homotopy equivalent spaces with equal homotopy groups?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 17, 2014 at 22:00 | history | edited | David White | CC BY-SA 3.0 |
Texified because it was on the front page anyway.
|
| Oct 31, 2009 at 14:00 | comment | added | Steven Sivek | Here's another example for the sake of originality: two 3-dimensional lens spaces L(p,q1) and L(p,q2) are homotopy equivalent iff q1*q2 = \pm n^2 (mod p) for some n, so L(5,1) and L(5,2) are not homotopy equivalent. But they both have fundamental group Z/5Z and universal cover S^3, so their homotopy groups are the same. | |
| Oct 31, 2009 at 13:59 | comment | added | Daniel Groves | I used the Wikipedia for this example... (But, yes it is the standard example, I think.) | |
| Oct 31, 2009 at 13:54 | comment | added | Steven Sivek | Beaten by 21 seconds -- I guess this really is a standard example! | |
| Oct 31, 2009 at 13:53 | history | answered | Steven Sivek | CC BY-SA 2.5 |